The fourth term of an ap is 37 and the sixth term is 12 more than the fourth term find the first and seventh term
Let's call the first term of the arithmetic progression a, and let's call the common difference d.
The fourth term of the arithmetic progression is given by a + 3d = 37.
The sixth term of the arithmetic progression is given by a + 5d = 37 + 12 = 49.
Now we have two equations with two variables:
a + 3d = 37,
a + 5d = 49.
We can solve these equations to find the values of a and d.
Subtracting the first equation from the second equation, we get:
(a + 5d) - (a + 3d) = 49 - 37,
2d = 12,
d = 6.
Substituting the value of d into the first equation, we get:
a + 3(6) = 37,
a + 18 = 37,
a = 37 - 18,
a = 19.
So the first term of the arithmetic progression is 19, and the common difference is 6.
The seventh term of the arithmetic progression is given by a + 6d = 19 + 6(6) = 19 + 36 = 55.
Therefore, the first term is 19 and the seventh term is 55.